At a wrestling competition, there are 4 competitors, and each competitor chooses a song to be played as they enter the arena. They all choose different songs because they don’t want to be confused with any of the other competitors.

Unfortunately, as they enter, the sound system just plays the songs in a random order, rather than matching the song to the competitor. What is the probability that none of the wrestlers have the correct song played for them?

What if there are 5 competitors? Or 6?